Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0120261703\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39399 | −1.69281 | −0.846405 | − | 0.532540i | \(-0.821238\pi\) | ||||
−0.846405 | + | 0.532540i | \(0.821238\pi\) | |||||||
\(3\) | 1.52449 | 0.880165 | 0.440082 | − | 0.897957i | \(-0.354949\pi\) | ||||
0.440082 | + | 0.897957i | \(0.354949\pi\) | |||||||
\(4\) | 3.73121 | 1.86560 | ||||||||
\(5\) | −2.51919 | −1.12662 | −0.563308 | − | 0.826247i | \(-0.690472\pi\) | ||||
−0.563308 | + | 0.826247i | \(0.690472\pi\) | |||||||
\(6\) | −3.64962 | −1.48995 | ||||||||
\(7\) | −1.00997 | −0.381732 | −0.190866 | − | 0.981616i | \(-0.561130\pi\) | ||||
−0.190866 | + | 0.981616i | \(0.561130\pi\) | |||||||
\(8\) | −4.14450 | −1.46530 | ||||||||
\(9\) | −0.675931 | −0.225310 | ||||||||
\(10\) | 6.03093 | 1.90715 | ||||||||
\(11\) | 1.01663 | 0.306524 | 0.153262 | − | 0.988186i | \(-0.451022\pi\) | ||||
0.153262 | + | 0.988186i | \(0.451022\pi\) | |||||||
\(12\) | 5.68819 | 1.64204 | ||||||||
\(13\) | −6.16777 | −1.71063 | −0.855315 | − | 0.518108i | \(-0.826637\pi\) | ||||
−0.855315 | + | 0.518108i | \(0.826637\pi\) | |||||||
\(14\) | 2.41786 | 0.646199 | ||||||||
\(15\) | −3.84048 | −0.991608 | ||||||||
\(16\) | 2.45950 | 0.614874 | ||||||||
\(17\) | −0.961955 | −0.233308 | −0.116654 | − | 0.993173i | \(-0.537217\pi\) | ||||
−0.116654 | + | 0.993173i | \(0.537217\pi\) | |||||||
\(18\) | 1.61818 | 0.381408 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −9.39963 | −2.10182 | ||||||||
\(21\) | −1.53968 | −0.335987 | ||||||||
\(22\) | −2.43379 | −0.518887 | ||||||||
\(23\) | −4.71882 | −0.983943 | −0.491971 | − | 0.870611i | \(-0.663724\pi\) | ||||
−0.491971 | + | 0.870611i | \(0.663724\pi\) | |||||||
\(24\) | −6.31825 | −1.28971 | ||||||||
\(25\) | 1.34633 | 0.269265 | ||||||||
\(26\) | 14.7656 | 2.89577 | ||||||||
\(27\) | −5.60392 | −1.07847 | ||||||||
\(28\) | −3.76840 | −0.712160 | ||||||||
\(29\) | 0.466130 | 0.0865582 | 0.0432791 | − | 0.999063i | \(-0.486220\pi\) | ||||
0.0432791 | + | 0.999063i | \(0.486220\pi\) | |||||||
\(30\) | 9.19409 | 1.67860 | ||||||||
\(31\) | −7.02934 | −1.26251 | −0.631253 | − | 0.775577i | \(-0.717459\pi\) | ||||
−0.631253 | + | 0.775577i | \(0.717459\pi\) | |||||||
\(32\) | 2.40098 | 0.424438 | ||||||||
\(33\) | 1.54983 | 0.269792 | ||||||||
\(34\) | 2.30292 | 0.394947 | ||||||||
\(35\) | 2.54430 | 0.430065 | ||||||||
\(36\) | −2.52204 | −0.420340 | ||||||||
\(37\) | 5.24361 | 0.862044 | 0.431022 | − | 0.902341i | \(-0.358153\pi\) | ||||
0.431022 | + | 0.902341i | \(0.358153\pi\) | |||||||
\(38\) | −2.39399 | −0.388357 | ||||||||
\(39\) | −9.40270 | −1.50564 | ||||||||
\(40\) | 10.4408 | 1.65083 | ||||||||
\(41\) | −8.70221 | −1.35906 | −0.679528 | − | 0.733649i | \(-0.737816\pi\) | ||||
−0.679528 | + | 0.733649i | \(0.737816\pi\) | |||||||
\(42\) | 3.68600 | 0.568761 | ||||||||
\(43\) | 5.38819 | 0.821691 | 0.410845 | − | 0.911705i | \(-0.365234\pi\) | ||||
0.410845 | + | 0.911705i | \(0.365234\pi\) | |||||||
\(44\) | 3.79324 | 0.571852 | ||||||||
\(45\) | 1.70280 | 0.253838 | ||||||||
\(46\) | 11.2968 | 1.66563 | ||||||||
\(47\) | 6.30953 | 0.920339 | 0.460170 | − | 0.887831i | \(-0.347789\pi\) | ||||
0.460170 | + | 0.887831i | \(0.347789\pi\) | |||||||
\(48\) | 3.74948 | 0.541190 | ||||||||
\(49\) | −5.97997 | −0.854281 | ||||||||
\(50\) | −3.22310 | −0.455815 | ||||||||
\(51\) | −1.46649 | −0.205350 | ||||||||
\(52\) | −23.0132 | −3.19136 | ||||||||
\(53\) | 5.52900 | 0.759467 | 0.379733 | − | 0.925096i | \(-0.376016\pi\) | ||||
0.379733 | + | 0.925096i | \(0.376016\pi\) | |||||||
\(54\) | 13.4157 | 1.82565 | ||||||||
\(55\) | −2.56107 | −0.345335 | ||||||||
\(56\) | 4.18581 | 0.559352 | ||||||||
\(57\) | 1.52449 | 0.201924 | ||||||||
\(58\) | −1.11591 | −0.146526 | ||||||||
\(59\) | 4.06983 | 0.529847 | 0.264923 | − | 0.964269i | \(-0.414653\pi\) | ||||
0.264923 | + | 0.964269i | \(0.414653\pi\) | |||||||
\(60\) | −14.3296 | −1.84995 | ||||||||
\(61\) | 0.502132 | 0.0642914 | 0.0321457 | − | 0.999483i | \(-0.489766\pi\) | ||||
0.0321457 | + | 0.999483i | \(0.489766\pi\) | |||||||
\(62\) | 16.8282 | 2.13718 | ||||||||
\(63\) | 0.682668 | 0.0860081 | ||||||||
\(64\) | −10.6669 | −1.33337 | ||||||||
\(65\) | 15.5378 | 1.92723 | ||||||||
\(66\) | −3.71029 | −0.456706 | ||||||||
\(67\) | −4.59271 | −0.561088 | −0.280544 | − | 0.959841i | \(-0.590515\pi\) | ||||
−0.280544 | + | 0.959841i | \(0.590515\pi\) | |||||||
\(68\) | −3.58925 | −0.435261 | ||||||||
\(69\) | −7.19380 | −0.866031 | ||||||||
\(70\) | −6.09104 | −0.728019 | ||||||||
\(71\) | 13.8847 | 1.64781 | 0.823905 | − | 0.566728i | \(-0.191791\pi\) | ||||
0.823905 | + | 0.566728i | \(0.191791\pi\) | |||||||
\(72\) | 2.80140 | 0.330148 | ||||||||
\(73\) | −10.1040 | −1.18258 | −0.591292 | − | 0.806457i | \(-0.701382\pi\) | ||||
−0.591292 | + | 0.806457i | \(0.701382\pi\) | |||||||
\(74\) | −12.5532 | −1.45928 | ||||||||
\(75\) | 2.05246 | 0.236998 | ||||||||
\(76\) | 3.73121 | 0.427999 | ||||||||
\(77\) | −1.02676 | −0.117010 | ||||||||
\(78\) | 22.5100 | 2.54876 | ||||||||
\(79\) | −5.90648 | −0.664530 | −0.332265 | − | 0.943186i | \(-0.607813\pi\) | ||||
−0.332265 | + | 0.943186i | \(0.607813\pi\) | |||||||
\(80\) | −6.19594 | −0.692727 | ||||||||
\(81\) | −6.51532 | −0.723925 | ||||||||
\(82\) | 20.8330 | 2.30062 | ||||||||
\(83\) | −9.85377 | −1.08159 | −0.540796 | − | 0.841154i | \(-0.681877\pi\) | ||||
−0.540796 | + | 0.841154i | \(0.681877\pi\) | |||||||
\(84\) | −5.74488 | −0.626818 | ||||||||
\(85\) | 2.42335 | 0.262849 | ||||||||
\(86\) | −12.8993 | −1.39097 | ||||||||
\(87\) | 0.710610 | 0.0761854 | ||||||||
\(88\) | −4.21340 | −0.449150 | ||||||||
\(89\) | 4.69318 | 0.497476 | 0.248738 | − | 0.968571i | \(-0.419984\pi\) | ||||
0.248738 | + | 0.968571i | \(0.419984\pi\) | |||||||
\(90\) | −4.07649 | −0.429700 | ||||||||
\(91\) | 6.22924 | 0.653002 | ||||||||
\(92\) | −17.6069 | −1.83565 | ||||||||
\(93\) | −10.7162 | −1.11121 | ||||||||
\(94\) | −15.1050 | −1.55796 | ||||||||
\(95\) | −2.51919 | −0.258464 | ||||||||
\(96\) | 3.66028 | 0.373575 | ||||||||
\(97\) | −6.31958 | −0.641656 | −0.320828 | − | 0.947137i | \(-0.603961\pi\) | ||||
−0.320828 | + | 0.947137i | \(0.603961\pi\) | |||||||
\(98\) | 14.3160 | 1.44613 | ||||||||
\(99\) | −0.687169 | −0.0690630 | ||||||||
\(100\) | 5.02342 | 0.502342 | ||||||||
\(101\) | 15.0638 | 1.49890 | 0.749451 | − | 0.662060i | \(-0.230318\pi\) | ||||
0.749451 | + | 0.662060i | \(0.230318\pi\) | |||||||
\(102\) | 3.51077 | 0.347618 | ||||||||
\(103\) | −3.00494 | −0.296085 | −0.148043 | − | 0.988981i | \(-0.547297\pi\) | ||||
−0.148043 | + | 0.988981i | \(0.547297\pi\) | |||||||
\(104\) | 25.5623 | 2.50659 | ||||||||
\(105\) | 3.87876 | 0.378528 | ||||||||
\(106\) | −13.2364 | −1.28563 | ||||||||
\(107\) | 8.90549 | 0.860927 | 0.430463 | − | 0.902608i | \(-0.358350\pi\) | ||||
0.430463 | + | 0.902608i | \(0.358350\pi\) | |||||||
\(108\) | −20.9094 | −2.01201 | ||||||||
\(109\) | 9.07859 | 0.869571 | 0.434786 | − | 0.900534i | \(-0.356824\pi\) | ||||
0.434786 | + | 0.900534i | \(0.356824\pi\) | |||||||
\(110\) | 6.13120 | 0.584587 | ||||||||
\(111\) | 7.99383 | 0.758741 | ||||||||
\(112\) | −2.48401 | −0.234717 | ||||||||
\(113\) | 0.245585 | 0.0231027 | 0.0115513 | − | 0.999933i | \(-0.496323\pi\) | ||||
0.0115513 | + | 0.999933i | \(0.496323\pi\) | |||||||
\(114\) | −3.64962 | −0.341818 | ||||||||
\(115\) | 11.8876 | 1.10853 | ||||||||
\(116\) | 1.73923 | 0.161483 | ||||||||
\(117\) | 4.16899 | 0.385423 | ||||||||
\(118\) | −9.74315 | −0.896930 | ||||||||
\(119\) | 0.971543 | 0.0890612 | ||||||||
\(120\) | 15.9169 | 1.45301 | ||||||||
\(121\) | −9.96647 | −0.906043 | ||||||||
\(122\) | −1.20210 | −0.108833 | ||||||||
\(123\) | −13.2664 | −1.19619 | ||||||||
\(124\) | −26.2279 | −2.35534 | ||||||||
\(125\) | 9.20430 | 0.823258 | ||||||||
\(126\) | −1.63430 | −0.145595 | ||||||||
\(127\) | 3.74558 | 0.332366 | 0.166183 | − | 0.986095i | \(-0.446856\pi\) | ||||
0.166183 | + | 0.986095i | \(0.446856\pi\) | |||||||
\(128\) | 20.7346 | 1.83270 | ||||||||
\(129\) | 8.21423 | 0.723223 | ||||||||
\(130\) | −37.1974 | −3.26243 | ||||||||
\(131\) | 16.8844 | 1.47520 | 0.737599 | − | 0.675239i | \(-0.235960\pi\) | ||||
0.737599 | + | 0.675239i | \(0.235960\pi\) | |||||||
\(132\) | 5.78275 | 0.503324 | ||||||||
\(133\) | −1.00997 | −0.0875753 | ||||||||
\(134\) | 10.9949 | 0.949816 | ||||||||
\(135\) | 14.1173 | 1.21503 | ||||||||
\(136\) | 3.98682 | 0.341867 | ||||||||
\(137\) | −21.2002 | −1.81126 | −0.905629 | − | 0.424070i | \(-0.860601\pi\) | ||||
−0.905629 | + | 0.424070i | \(0.860601\pi\) | |||||||
\(138\) | 17.2219 | 1.46603 | ||||||||
\(139\) | 8.61031 | 0.730317 | 0.365159 | − | 0.930945i | \(-0.381015\pi\) | ||||
0.365159 | + | 0.930945i | \(0.381015\pi\) | |||||||
\(140\) | 9.49331 | 0.802332 | ||||||||
\(141\) | 9.61881 | 0.810050 | ||||||||
\(142\) | −33.2399 | −2.78943 | ||||||||
\(143\) | −6.27031 | −0.524349 | ||||||||
\(144\) | −1.66245 | −0.138537 | ||||||||
\(145\) | −1.17427 | −0.0975179 | ||||||||
\(146\) | 24.1889 | 2.00189 | ||||||||
\(147\) | −9.11640 | −0.751908 | ||||||||
\(148\) | 19.5650 | 1.60823 | ||||||||
\(149\) | −3.13227 | −0.256606 | −0.128303 | − | 0.991735i | \(-0.540953\pi\) | ||||
−0.128303 | + | 0.991735i | \(0.540953\pi\) | |||||||
\(150\) | −4.91358 | −0.401192 | ||||||||
\(151\) | −12.1668 | −0.990119 | −0.495060 | − | 0.868859i | \(-0.664854\pi\) | ||||
−0.495060 | + | 0.868859i | \(0.664854\pi\) | |||||||
\(152\) | −4.14450 | −0.336163 | ||||||||
\(153\) | 0.650215 | 0.0525668 | ||||||||
\(154\) | 2.45805 | 0.198076 | ||||||||
\(155\) | 17.7082 | 1.42236 | ||||||||
\(156\) | −35.0834 | −2.80892 | ||||||||
\(157\) | 15.3628 | 1.22608 | 0.613041 | − | 0.790051i | \(-0.289946\pi\) | ||||
0.613041 | + | 0.790051i | \(0.289946\pi\) | |||||||
\(158\) | 14.1401 | 1.12492 | ||||||||
\(159\) | 8.42890 | 0.668456 | ||||||||
\(160\) | −6.04854 | −0.478179 | ||||||||
\(161\) | 4.76586 | 0.375602 | ||||||||
\(162\) | 15.5976 | 1.22547 | ||||||||
\(163\) | 8.17768 | 0.640525 | 0.320263 | − | 0.947329i | \(-0.396229\pi\) | ||||
0.320263 | + | 0.947329i | \(0.396229\pi\) | |||||||
\(164\) | −32.4698 | −2.53546 | ||||||||
\(165\) | −3.90433 | −0.303952 | ||||||||
\(166\) | 23.5899 | 1.83093 | ||||||||
\(167\) | 18.2963 | 1.41581 | 0.707903 | − | 0.706309i | \(-0.249641\pi\) | ||||
0.707903 | + | 0.706309i | \(0.249641\pi\) | |||||||
\(168\) | 6.38122 | 0.492322 | ||||||||
\(169\) | 25.0413 | 1.92626 | ||||||||
\(170\) | −5.80148 | −0.444954 | ||||||||
\(171\) | −0.675931 | −0.0516897 | ||||||||
\(172\) | 20.1044 | 1.53295 | ||||||||
\(173\) | −14.6066 | −1.11052 | −0.555258 | − | 0.831678i | \(-0.687381\pi\) | ||||
−0.555258 | + | 0.831678i | \(0.687381\pi\) | |||||||
\(174\) | −1.70120 | −0.128967 | ||||||||
\(175\) | −1.35975 | −0.102787 | ||||||||
\(176\) | 2.50039 | 0.188474 | ||||||||
\(177\) | 6.20441 | 0.466352 | ||||||||
\(178\) | −11.2354 | −0.842132 | ||||||||
\(179\) | −0.802680 | −0.0599951 | −0.0299976 | − | 0.999550i | \(-0.509550\pi\) | ||||
−0.0299976 | + | 0.999550i | \(0.509550\pi\) | |||||||
\(180\) | 6.35350 | 0.473562 | ||||||||
\(181\) | 1.76105 | 0.130898 | 0.0654489 | − | 0.997856i | \(-0.479152\pi\) | ||||
0.0654489 | + | 0.997856i | \(0.479152\pi\) | |||||||
\(182\) | −14.9128 | −1.10541 | ||||||||
\(183\) | 0.765494 | 0.0565870 | ||||||||
\(184\) | 19.5572 | 1.44177 | ||||||||
\(185\) | −13.2097 | −0.971194 | ||||||||
\(186\) | 25.6544 | 1.88107 | ||||||||
\(187\) | −0.977948 | −0.0715146 | ||||||||
\(188\) | 23.5422 | 1.71699 | ||||||||
\(189\) | 5.65977 | 0.411688 | ||||||||
\(190\) | 6.03093 | 0.437530 | ||||||||
\(191\) | −17.4284 | −1.26108 | −0.630539 | − | 0.776158i | \(-0.717166\pi\) | ||||
−0.630539 | + | 0.776158i | \(0.717166\pi\) | |||||||
\(192\) | −16.2616 | −1.17358 | ||||||||
\(193\) | −14.7500 | −1.06173 | −0.530863 | − | 0.847458i | \(-0.678132\pi\) | ||||
−0.530863 | + | 0.847458i | \(0.678132\pi\) | |||||||
\(194\) | 15.1290 | 1.08620 | ||||||||
\(195\) | 23.6872 | 1.69628 | ||||||||
\(196\) | −22.3125 | −1.59375 | ||||||||
\(197\) | 16.5806 | 1.18132 | 0.590659 | − | 0.806921i | \(-0.298868\pi\) | ||||
0.590659 | + | 0.806921i | \(0.298868\pi\) | |||||||
\(198\) | 1.64508 | 0.116911 | ||||||||
\(199\) | 24.9698 | 1.77006 | 0.885032 | − | 0.465531i | \(-0.154137\pi\) | ||||
0.885032 | + | 0.465531i | \(0.154137\pi\) | |||||||
\(200\) | −5.57985 | −0.394555 | ||||||||
\(201\) | −7.00153 | −0.493850 | ||||||||
\(202\) | −36.0626 | −2.53735 | ||||||||
\(203\) | −0.470776 | −0.0330420 | ||||||||
\(204\) | −5.47178 | −0.383101 | ||||||||
\(205\) | 21.9225 | 1.53114 | ||||||||
\(206\) | 7.19380 | 0.501216 | ||||||||
\(207\) | 3.18960 | 0.221692 | ||||||||
\(208\) | −15.1696 | −1.05182 | ||||||||
\(209\) | 1.01663 | 0.0703214 | ||||||||
\(210\) | −9.28573 | −0.640776 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 20.6298 | 1.41686 | ||||||||
\(213\) | 21.1671 | 1.45034 | ||||||||
\(214\) | −21.3197 | −1.45738 | ||||||||
\(215\) | −13.5739 | −0.925730 | ||||||||
\(216\) | 23.2254 | 1.58029 | ||||||||
\(217\) | 7.09940 | 0.481939 | ||||||||
\(218\) | −21.7341 | −1.47202 | ||||||||
\(219\) | −15.4035 | −1.04087 | ||||||||
\(220\) | −9.55590 | −0.644258 | ||||||||
\(221\) | 5.93312 | 0.399105 | ||||||||
\(222\) | −19.1372 | −1.28440 | ||||||||
\(223\) | −14.2568 | −0.954706 | −0.477353 | − | 0.878712i | \(-0.658404\pi\) | ||||
−0.477353 | + | 0.878712i | \(0.658404\pi\) | |||||||
\(224\) | −2.42491 | −0.162021 | ||||||||
\(225\) | −0.910024 | −0.0606683 | ||||||||
\(226\) | −0.587929 | −0.0391085 | ||||||||
\(227\) | −12.4302 | −0.825022 | −0.412511 | − | 0.910953i | \(-0.635348\pi\) | ||||
−0.412511 | + | 0.910953i | \(0.635348\pi\) | |||||||
\(228\) | 5.68819 | 0.376709 | ||||||||
\(229\) | 22.0750 | 1.45875 | 0.729377 | − | 0.684112i | \(-0.239810\pi\) | ||||
0.729377 | + | 0.684112i | \(0.239810\pi\) | |||||||
\(230\) | −28.4589 | −1.87652 | ||||||||
\(231\) | −1.56528 | −0.102988 | ||||||||
\(232\) | −1.93188 | −0.126834 | ||||||||
\(233\) | 12.6830 | 0.830892 | 0.415446 | − | 0.909618i | \(-0.363626\pi\) | ||||
0.415446 | + | 0.909618i | \(0.363626\pi\) | |||||||
\(234\) | −9.98053 | −0.652447 | ||||||||
\(235\) | −15.8949 | −1.03687 | ||||||||
\(236\) | 15.1854 | 0.988484 | ||||||||
\(237\) | −9.00436 | −0.584896 | ||||||||
\(238\) | −2.32587 | −0.150764 | ||||||||
\(239\) | −2.20619 | −0.142706 | −0.0713532 | − | 0.997451i | \(-0.522732\pi\) | ||||
−0.0713532 | + | 0.997451i | \(0.522732\pi\) | |||||||
\(240\) | −9.44565 | −0.609714 | ||||||||
\(241\) | 14.6666 | 0.944760 | 0.472380 | − | 0.881395i | \(-0.343395\pi\) | ||||
0.472380 | + | 0.881395i | \(0.343395\pi\) | |||||||
\(242\) | 23.8597 | 1.53376 | ||||||||
\(243\) | 6.87921 | 0.441302 | ||||||||
\(244\) | 1.87356 | 0.119942 | ||||||||
\(245\) | 15.0647 | 0.962447 | ||||||||
\(246\) | 31.7598 | 2.02493 | ||||||||
\(247\) | −6.16777 | −0.392446 | ||||||||
\(248\) | 29.1331 | 1.84995 | ||||||||
\(249\) | −15.0220 | −0.951979 | ||||||||
\(250\) | −22.0350 | −1.39362 | ||||||||
\(251\) | 5.91049 | 0.373067 | 0.186534 | − | 0.982449i | \(-0.440275\pi\) | ||||
0.186534 | + | 0.982449i | \(0.440275\pi\) | |||||||
\(252\) | 2.54718 | 0.160457 | ||||||||
\(253\) | −4.79727 | −0.301602 | ||||||||
\(254\) | −8.96689 | −0.562632 | ||||||||
\(255\) | 3.69437 | 0.231351 | ||||||||
\(256\) | −28.3047 | −1.76904 | ||||||||
\(257\) | −16.1650 | −1.00835 | −0.504173 | − | 0.863603i | \(-0.668203\pi\) | ||||
−0.504173 | + | 0.863603i | \(0.668203\pi\) | |||||||
\(258\) | −19.6648 | −1.22428 | ||||||||
\(259\) | −5.29588 | −0.329070 | ||||||||
\(260\) | 57.9747 | 3.59544 | ||||||||
\(261\) | −0.315072 | −0.0195025 | ||||||||
\(262\) | −40.4212 | −2.49723 | ||||||||
\(263\) | −26.0675 | −1.60739 | −0.803697 | − | 0.595039i | \(-0.797137\pi\) | ||||
−0.803697 | + | 0.595039i | \(0.797137\pi\) | |||||||
\(264\) | −6.42329 | −0.395326 | ||||||||
\(265\) | −13.9286 | −0.855628 | ||||||||
\(266\) | 2.41786 | 0.148248 | ||||||||
\(267\) | 7.15470 | 0.437861 | ||||||||
\(268\) | −17.1363 | −1.04677 | ||||||||
\(269\) | −15.4349 | −0.941085 | −0.470542 | − | 0.882377i | \(-0.655942\pi\) | ||||
−0.470542 | + | 0.882377i | \(0.655942\pi\) | |||||||
\(270\) | −33.7968 | −2.05681 | ||||||||
\(271\) | 5.02852 | 0.305461 | 0.152730 | − | 0.988268i | \(-0.451193\pi\) | ||||
0.152730 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(272\) | −2.36592 | −0.143455 | ||||||||
\(273\) | 9.49642 | 0.574749 | ||||||||
\(274\) | 50.7532 | 3.06612 | ||||||||
\(275\) | 1.36871 | 0.0825363 | ||||||||
\(276\) | −26.8416 | −1.61567 | ||||||||
\(277\) | −5.50274 | −0.330628 | −0.165314 | − | 0.986241i | \(-0.552864\pi\) | ||||
−0.165314 | + | 0.986241i | \(0.552864\pi\) | |||||||
\(278\) | −20.6130 | −1.23629 | ||||||||
\(279\) | 4.75135 | 0.284456 | ||||||||
\(280\) | −10.5449 | −0.630176 | ||||||||
\(281\) | 30.4919 | 1.81899 | 0.909497 | − | 0.415710i | \(-0.136467\pi\) | ||||
0.909497 | + | 0.415710i | \(0.136467\pi\) | |||||||
\(282\) | −23.0274 | −1.37126 | ||||||||
\(283\) | −29.2984 | −1.74161 | −0.870806 | − | 0.491627i | \(-0.836402\pi\) | ||||
−0.870806 | + | 0.491627i | \(0.836402\pi\) | |||||||
\(284\) | 51.8067 | 3.07416 | ||||||||
\(285\) | −3.84048 | −0.227491 | ||||||||
\(286\) | 15.0111 | 0.887624 | ||||||||
\(287\) | 8.78895 | 0.518795 | ||||||||
\(288\) | −1.62290 | −0.0956303 | ||||||||
\(289\) | −16.0746 | −0.945567 | ||||||||
\(290\) | 2.81120 | 0.165079 | ||||||||
\(291\) | −9.63413 | −0.564763 | ||||||||
\(292\) | −37.7001 | −2.20623 | ||||||||
\(293\) | 31.3277 | 1.83018 | 0.915090 | − | 0.403249i | \(-0.132119\pi\) | ||||
0.915090 | + | 0.403249i | \(0.132119\pi\) | |||||||
\(294\) | 21.8246 | 1.27284 | ||||||||
\(295\) | −10.2527 | −0.596934 | ||||||||
\(296\) | −21.7322 | −1.26316 | ||||||||
\(297\) | −5.69709 | −0.330578 | ||||||||
\(298\) | 7.49864 | 0.434385 | ||||||||
\(299\) | 29.1046 | 1.68316 | ||||||||
\(300\) | 7.65816 | 0.442144 | ||||||||
\(301\) | −5.44189 | −0.313665 | ||||||||
\(302\) | 29.1272 | 1.67608 | ||||||||
\(303\) | 22.9646 | 1.31928 | ||||||||
\(304\) | 2.45950 | 0.141062 | ||||||||
\(305\) | −1.26497 | −0.0724317 | ||||||||
\(306\) | −1.55661 | −0.0889856 | ||||||||
\(307\) | −18.9351 | −1.08069 | −0.540343 | − | 0.841445i | \(-0.681705\pi\) | ||||
−0.540343 | + | 0.841445i | \(0.681705\pi\) | |||||||
\(308\) | −3.83105 | −0.218294 | ||||||||
\(309\) | −4.58100 | −0.260604 | ||||||||
\(310\) | −42.3934 | −2.40779 | ||||||||
\(311\) | −24.7482 | −1.40334 | −0.701670 | − | 0.712502i | \(-0.747562\pi\) | ||||
−0.701670 | + | 0.712502i | \(0.747562\pi\) | |||||||
\(312\) | 38.9695 | 2.20621 | ||||||||
\(313\) | 5.02782 | 0.284189 | 0.142095 | − | 0.989853i | \(-0.454616\pi\) | ||||
0.142095 | + | 0.989853i | \(0.454616\pi\) | |||||||
\(314\) | −36.7784 | −2.07552 | ||||||||
\(315\) | −1.71977 | −0.0968982 | ||||||||
\(316\) | −22.0383 | −1.23975 | ||||||||
\(317\) | −11.1787 | −0.627860 | −0.313930 | − | 0.949446i | \(-0.601646\pi\) | ||||
−0.313930 | + | 0.949446i | \(0.601646\pi\) | |||||||
\(318\) | −20.1787 | −1.13157 | ||||||||
\(319\) | 0.473880 | 0.0265322 | ||||||||
\(320\) | 26.8720 | 1.50219 | ||||||||
\(321\) | 13.5763 | 0.757757 | ||||||||
\(322\) | −11.4094 | −0.635823 | ||||||||
\(323\) | −0.961955 | −0.0535246 | ||||||||
\(324\) | −24.3100 | −1.35056 | ||||||||
\(325\) | −8.30383 | −0.460614 | ||||||||
\(326\) | −19.5773 | −1.08429 | ||||||||
\(327\) | 13.8402 | 0.765366 | ||||||||
\(328\) | 36.0663 | 1.99143 | ||||||||
\(329\) | −6.37242 | −0.351323 | ||||||||
\(330\) | 9.34694 | 0.514532 | ||||||||
\(331\) | −23.4557 | −1.28924 | −0.644622 | − | 0.764501i | \(-0.722985\pi\) | ||||
−0.644622 | + | 0.764501i | \(0.722985\pi\) | |||||||
\(332\) | −36.7665 | −2.01782 | ||||||||
\(333\) | −3.54432 | −0.194228 | ||||||||
\(334\) | −43.8011 | −2.39669 | ||||||||
\(335\) | 11.5699 | 0.632132 | ||||||||
\(336\) | −3.78685 | −0.206589 | ||||||||
\(337\) | −25.5783 | −1.39334 | −0.696669 | − | 0.717392i | \(-0.745336\pi\) | ||||
−0.696669 | + | 0.717392i | \(0.745336\pi\) | |||||||
\(338\) | −59.9488 | −3.26079 | ||||||||
\(339\) | 0.374392 | 0.0203342 | ||||||||
\(340\) | 9.04202 | 0.490372 | ||||||||
\(341\) | −7.14620 | −0.386989 | ||||||||
\(342\) | 1.61818 | 0.0875009 | ||||||||
\(343\) | 13.1093 | 0.707838 | ||||||||
\(344\) | −22.3313 | −1.20403 | ||||||||
\(345\) | 18.1226 | 0.975685 | ||||||||
\(346\) | 34.9680 | 1.87989 | ||||||||
\(347\) | −15.2290 | −0.817537 | −0.408768 | − | 0.912638i | \(-0.634042\pi\) | ||||
−0.408768 | + | 0.912638i | \(0.634042\pi\) | |||||||
\(348\) | 2.65144 | 0.142132 | ||||||||
\(349\) | 10.3873 | 0.556019 | 0.278010 | − | 0.960578i | \(-0.410325\pi\) | ||||
0.278010 | + | 0.960578i | \(0.410325\pi\) | |||||||
\(350\) | 3.25522 | 0.173999 | ||||||||
\(351\) | 34.5637 | 1.84487 | ||||||||
\(352\) | 2.44090 | 0.130100 | ||||||||
\(353\) | 22.6795 | 1.20711 | 0.603555 | − | 0.797321i | \(-0.293750\pi\) | ||||
0.603555 | + | 0.797321i | \(0.293750\pi\) | |||||||
\(354\) | −14.8533 | −0.789446 | ||||||||
\(355\) | −34.9782 | −1.85645 | ||||||||
\(356\) | 17.5112 | 0.928093 | ||||||||
\(357\) | 1.48111 | 0.0783885 | ||||||||
\(358\) | 1.92161 | 0.101560 | ||||||||
\(359\) | 26.9195 | 1.42076 | 0.710378 | − | 0.703820i | \(-0.248524\pi\) | ||||
0.710378 | + | 0.703820i | \(0.248524\pi\) | |||||||
\(360\) | −7.05726 | −0.371950 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −4.21594 | −0.221585 | ||||||||
\(363\) | −15.1938 | −0.797467 | ||||||||
\(364\) | 23.2426 | 1.21824 | ||||||||
\(365\) | 25.4539 | 1.33232 | ||||||||
\(366\) | −1.83259 | −0.0957910 | ||||||||
\(367\) | −23.1032 | −1.20598 | −0.602988 | − | 0.797750i | \(-0.706023\pi\) | ||||
−0.602988 | + | 0.797750i | \(0.706023\pi\) | |||||||
\(368\) | −11.6059 | −0.605001 | ||||||||
\(369\) | 5.88209 | 0.306210 | ||||||||
\(370\) | 31.6239 | 1.64405 | ||||||||
\(371\) | −5.58411 | −0.289912 | ||||||||
\(372\) | −39.9842 | −2.07308 | ||||||||
\(373\) | 17.6456 | 0.913653 | 0.456827 | − | 0.889556i | \(-0.348986\pi\) | ||||
0.456827 | + | 0.889556i | \(0.348986\pi\) | |||||||
\(374\) | 2.34120 | 0.121061 | ||||||||
\(375\) | 14.0319 | 0.724602 | ||||||||
\(376\) | −26.1498 | −1.34858 | ||||||||
\(377\) | −2.87498 | −0.148069 | ||||||||
\(378\) | −13.5495 | −0.696909 | ||||||||
\(379\) | 3.63529 | 0.186732 | 0.0933662 | − | 0.995632i | \(-0.470237\pi\) | ||||
0.0933662 | + | 0.995632i | \(0.470237\pi\) | |||||||
\(380\) | −9.39963 | −0.482191 | ||||||||
\(381\) | 5.71009 | 0.292537 | ||||||||
\(382\) | 41.7236 | 2.13476 | ||||||||
\(383\) | 17.0434 | 0.870877 | 0.435438 | − | 0.900219i | \(-0.356593\pi\) | ||||
0.435438 | + | 0.900219i | \(0.356593\pi\) | |||||||
\(384\) | 31.6097 | 1.61308 | ||||||||
\(385\) | 2.58660 | 0.131825 | ||||||||
\(386\) | 35.3113 | 1.79730 | ||||||||
\(387\) | −3.64204 | −0.185135 | ||||||||
\(388\) | −23.5797 | −1.19708 | ||||||||
\(389\) | 8.92973 | 0.452755 | 0.226378 | − | 0.974040i | \(-0.427312\pi\) | ||||
0.226378 | + | 0.974040i | \(0.427312\pi\) | |||||||
\(390\) | −56.7070 | −2.87147 | ||||||||
\(391\) | 4.53930 | 0.229562 | ||||||||
\(392\) | 24.7840 | 1.25178 | ||||||||
\(393\) | 25.7401 | 1.29842 | ||||||||
\(394\) | −39.6938 | −1.99975 | ||||||||
\(395\) | 14.8795 | 0.748671 | ||||||||
\(396\) | −2.56397 | −0.128844 | ||||||||
\(397\) | 17.9147 | 0.899111 | 0.449555 | − | 0.893252i | \(-0.351582\pi\) | ||||
0.449555 | + | 0.893252i | \(0.351582\pi\) | |||||||
\(398\) | −59.7776 | −2.99638 | ||||||||
\(399\) | −1.53968 | −0.0770806 | ||||||||
\(400\) | 3.31128 | 0.165564 | ||||||||
\(401\) | 16.0895 | 0.803473 | 0.401736 | − | 0.915755i | \(-0.368407\pi\) | ||||
0.401736 | + | 0.915755i | \(0.368407\pi\) | |||||||
\(402\) | 16.7616 | 0.835994 | ||||||||
\(403\) | 43.3553 | 2.15968 | ||||||||
\(404\) | 56.2061 | 2.79636 | ||||||||
\(405\) | 16.4133 | 0.815586 | ||||||||
\(406\) | 1.12703 | 0.0559338 | ||||||||
\(407\) | 5.33079 | 0.264237 | ||||||||
\(408\) | 6.07787 | 0.300900 | ||||||||
\(409\) | 19.7873 | 0.978421 | 0.489211 | − | 0.872166i | \(-0.337285\pi\) | ||||
0.489211 | + | 0.872166i | \(0.337285\pi\) | |||||||
\(410\) | −52.4824 | −2.59192 | ||||||||
\(411\) | −32.3195 | −1.59421 | ||||||||
\(412\) | −11.2120 | −0.552378 | ||||||||
\(413\) | −4.11039 | −0.202259 | ||||||||
\(414\) | −7.63588 | −0.375283 | ||||||||
\(415\) | 24.8235 | 1.21854 | ||||||||
\(416\) | −14.8087 | −0.726057 | ||||||||
\(417\) | 13.1263 | 0.642799 | ||||||||
\(418\) | −2.43379 | −0.119041 | ||||||||
\(419\) | 13.4321 | 0.656199 | 0.328099 | − | 0.944643i | \(-0.393592\pi\) | ||||
0.328099 | + | 0.944643i | \(0.393592\pi\) | |||||||
\(420\) | 14.4725 | 0.706184 | ||||||||
\(421\) | 12.9939 | 0.633284 | 0.316642 | − | 0.948545i | \(-0.397445\pi\) | ||||
0.316642 | + | 0.948545i | \(0.397445\pi\) | |||||||
\(422\) | 2.39399 | 0.116538 | ||||||||
\(423\) | −4.26481 | −0.207362 | ||||||||
\(424\) | −22.9149 | −1.11285 | ||||||||
\(425\) | −1.29511 | −0.0628219 | ||||||||
\(426\) | −50.6739 | −2.45516 | ||||||||
\(427\) | −0.507136 | −0.0245420 | ||||||||
\(428\) | 33.2282 | 1.60615 | ||||||||
\(429\) | −9.55902 | −0.461514 | ||||||||
\(430\) | 32.4958 | 1.56709 | ||||||||
\(431\) | 31.7065 | 1.52725 | 0.763623 | − | 0.645662i | \(-0.223419\pi\) | ||||
0.763623 | + | 0.645662i | \(0.223419\pi\) | |||||||
\(432\) | −13.7828 | −0.663126 | ||||||||
\(433\) | 2.80020 | 0.134569 | 0.0672845 | − | 0.997734i | \(-0.478566\pi\) | ||||
0.0672845 | + | 0.997734i | \(0.478566\pi\) | |||||||
\(434\) | −16.9959 | −0.815830 | ||||||||
\(435\) | −1.79016 | −0.0858318 | ||||||||
\(436\) | 33.8741 | 1.62228 | ||||||||
\(437\) | −4.71882 | −0.225732 | ||||||||
\(438\) | 36.8758 | 1.76199 | ||||||||
\(439\) | −3.34540 | −0.159667 | −0.0798337 | − | 0.996808i | \(-0.525439\pi\) | ||||
−0.0798337 | + | 0.996808i | \(0.525439\pi\) | |||||||
\(440\) | 10.6144 | 0.506020 | ||||||||
\(441\) | 4.04205 | 0.192478 | ||||||||
\(442\) | −14.2038 | −0.675608 | ||||||||
\(443\) | 11.9357 | 0.567084 | 0.283542 | − | 0.958960i | \(-0.408491\pi\) | ||||
0.283542 | + | 0.958960i | \(0.408491\pi\) | |||||||
\(444\) | 29.8266 | 1.41551 | ||||||||
\(445\) | −11.8230 | −0.560465 | ||||||||
\(446\) | 34.1307 | 1.61614 | ||||||||
\(447\) | −4.77512 | −0.225855 | ||||||||
\(448\) | 10.7733 | 0.508988 | ||||||||
\(449\) | 12.3046 | 0.580690 | 0.290345 | − | 0.956922i | \(-0.406230\pi\) | ||||
0.290345 | + | 0.956922i | \(0.406230\pi\) | |||||||
\(450\) | 2.17859 | 0.102700 | ||||||||
\(451\) | −8.84688 | −0.416584 | ||||||||
\(452\) | 0.916329 | 0.0431005 | ||||||||
\(453\) | −18.5481 | −0.871468 | ||||||||
\(454\) | 29.7578 | 1.39660 | ||||||||
\(455\) | −15.6927 | −0.735683 | ||||||||
\(456\) | −6.31825 | −0.295879 | ||||||||
\(457\) | 15.7677 | 0.737583 | 0.368791 | − | 0.929512i | \(-0.379772\pi\) | ||||
0.368791 | + | 0.929512i | \(0.379772\pi\) | |||||||
\(458\) | −52.8473 | −2.46939 | ||||||||
\(459\) | 5.39072 | 0.251617 | ||||||||
\(460\) | 44.3552 | 2.06807 | ||||||||
\(461\) | 13.0230 | 0.606543 | 0.303271 | − | 0.952904i | \(-0.401921\pi\) | ||||
0.303271 | + | 0.952904i | \(0.401921\pi\) | |||||||
\(462\) | 3.74728 | 0.174339 | ||||||||
\(463\) | 8.30575 | 0.386001 | 0.193000 | − | 0.981199i | \(-0.438178\pi\) | ||||
0.193000 | + | 0.981199i | \(0.438178\pi\) | |||||||
\(464\) | 1.14644 | 0.0532224 | ||||||||
\(465\) | 26.9960 | 1.25191 | ||||||||
\(466\) | −30.3630 | −1.40654 | ||||||||
\(467\) | −23.5531 | −1.08991 | −0.544953 | − | 0.838466i | \(-0.683453\pi\) | ||||
−0.544953 | + | 0.838466i | \(0.683453\pi\) | |||||||
\(468\) | 15.5554 | 0.719046 | ||||||||
\(469\) | 4.63848 | 0.214185 | ||||||||
\(470\) | 38.0523 | 1.75522 | ||||||||
\(471\) | 23.4204 | 1.07915 | ||||||||
\(472\) | −16.8674 | −0.776386 | ||||||||
\(473\) | 5.47776 | 0.251868 | ||||||||
\(474\) | 21.5564 | 0.990118 | ||||||||
\(475\) | 1.34633 | 0.0617737 | ||||||||
\(476\) | 3.62503 | 0.166153 | ||||||||
\(477\) | −3.73722 | −0.171116 | ||||||||
\(478\) | 5.28160 | 0.241575 | ||||||||
\(479\) | −26.5839 | −1.21465 | −0.607324 | − | 0.794454i | \(-0.707757\pi\) | ||||
−0.607324 | + | 0.794454i | \(0.707757\pi\) | |||||||
\(480\) | −9.22093 | −0.420876 | ||||||||
\(481\) | −32.3414 | −1.47464 | ||||||||
\(482\) | −35.1118 | −1.59930 | ||||||||
\(483\) | 7.26550 | 0.330592 | ||||||||
\(484\) | −37.1870 | −1.69032 | ||||||||
\(485\) | 15.9202 | 0.722900 | ||||||||
\(486\) | −16.4688 | −0.747040 | ||||||||
\(487\) | 15.2263 | 0.689967 | 0.344984 | − | 0.938609i | \(-0.387884\pi\) | ||||
0.344984 | + | 0.938609i | \(0.387884\pi\) | |||||||
\(488\) | −2.08108 | −0.0942063 | ||||||||
\(489\) | 12.4668 | 0.563768 | ||||||||
\(490\) | −36.0648 | −1.62924 | ||||||||
\(491\) | 21.5944 | 0.974543 | 0.487271 | − | 0.873251i | \(-0.337992\pi\) | ||||
0.487271 | + | 0.873251i | \(0.337992\pi\) | |||||||
\(492\) | −49.4998 | −2.23162 | ||||||||
\(493\) | −0.448396 | −0.0201948 | ||||||||
\(494\) | 14.7656 | 0.664336 | ||||||||
\(495\) | 1.73111 | 0.0778076 | ||||||||
\(496\) | −17.2886 | −0.776282 | ||||||||
\(497\) | −14.0231 | −0.629021 | ||||||||
\(498\) | 35.9625 | 1.61152 | ||||||||
\(499\) | 16.5485 | 0.740810 | 0.370405 | − | 0.928870i | \(-0.379219\pi\) | ||||
0.370405 | + | 0.928870i | \(0.379219\pi\) | |||||||
\(500\) | 34.3432 | 1.53587 | ||||||||
\(501\) | 27.8925 | 1.24614 | ||||||||
\(502\) | −14.1497 | −0.631532 | ||||||||
\(503\) | 10.6404 | 0.474432 | 0.237216 | − | 0.971457i | \(-0.423765\pi\) | ||||
0.237216 | + | 0.971457i | \(0.423765\pi\) | |||||||
\(504\) | −2.82932 | −0.126028 | ||||||||
\(505\) | −37.9485 | −1.68869 | ||||||||
\(506\) | 11.4846 | 0.510555 | ||||||||
\(507\) | 38.1753 | 1.69542 | ||||||||
\(508\) | 13.9755 | 0.620063 | ||||||||
\(509\) | 8.97296 | 0.397720 | 0.198860 | − | 0.980028i | \(-0.436276\pi\) | ||||
0.198860 | + | 0.980028i | \(0.436276\pi\) | |||||||
\(510\) | −8.84430 | −0.391632 | ||||||||
\(511\) | 10.2047 | 0.451430 | ||||||||
\(512\) | 26.2920 | 1.16195 | ||||||||
\(513\) | −5.60392 | −0.247419 | ||||||||
\(514\) | 38.6989 | 1.70694 | ||||||||
\(515\) | 7.57001 | 0.333575 | ||||||||
\(516\) | 30.6490 | 1.34925 | ||||||||
\(517\) | 6.41443 | 0.282106 | ||||||||
\(518\) | 12.6783 | 0.557052 | ||||||||
\(519\) | −22.2676 | −0.977438 | ||||||||
\(520\) | −64.3964 | −2.82397 | ||||||||
\(521\) | 13.6795 | 0.599311 | 0.299655 | − | 0.954048i | \(-0.403128\pi\) | ||||
0.299655 | + | 0.954048i | \(0.403128\pi\) | |||||||
\(522\) | 0.754280 | 0.0330139 | ||||||||
\(523\) | −5.19636 | −0.227221 | −0.113611 | − | 0.993525i | \(-0.536242\pi\) | ||||
−0.113611 | + | 0.993525i | \(0.536242\pi\) | |||||||
\(524\) | 62.9993 | 2.75214 | ||||||||
\(525\) | −2.07292 | −0.0904696 | ||||||||
\(526\) | 62.4055 | 2.72101 | ||||||||
\(527\) | 6.76191 | 0.294553 | ||||||||
\(528\) | 3.81181 | 0.165888 | ||||||||
\(529\) | −0.732711 | −0.0318570 | ||||||||
\(530\) | 33.3450 | 1.44841 | ||||||||
\(531\) | −2.75092 | −0.119380 | ||||||||
\(532\) | −3.76840 | −0.163381 | ||||||||
\(533\) | 53.6732 | 2.32484 | ||||||||
\(534\) | −17.1283 | −0.741215 | ||||||||
\(535\) | −22.4346 | −0.969934 | ||||||||
\(536\) | 19.0345 | 0.822164 | ||||||||
\(537\) | −1.22368 | −0.0528056 | ||||||||
\(538\) | 36.9512 | 1.59308 | ||||||||
\(539\) | −6.07938 | −0.261858 | ||||||||
\(540\) | 52.6748 | 2.26676 | ||||||||
\(541\) | 5.54278 | 0.238303 | 0.119151 | − | 0.992876i | \(-0.461983\pi\) | ||||
0.119151 | + | 0.992876i | \(0.461983\pi\) | |||||||
\(542\) | −12.0383 | −0.517087 | ||||||||
\(543\) | 2.68470 | 0.115212 | ||||||||
\(544\) | −2.30964 | −0.0990250 | ||||||||
\(545\) | −22.8707 | −0.979673 | ||||||||
\(546\) | −22.7344 | −0.972941 | ||||||||
\(547\) | 30.2873 | 1.29499 | 0.647496 | − | 0.762069i | \(-0.275816\pi\) | ||||
0.647496 | + | 0.762069i | \(0.275816\pi\) | |||||||
\(548\) | −79.1025 | −3.37909 | ||||||||
\(549\) | −0.339406 | −0.0144855 | ||||||||
\(550\) | −3.27668 | −0.139718 | ||||||||
\(551\) | 0.466130 | 0.0198578 | ||||||||
\(552\) | 29.8147 | 1.26900 | ||||||||
\(553\) | 5.96535 | 0.253672 | ||||||||
\(554\) | 13.1735 | 0.559690 | ||||||||
\(555\) | −20.1380 | −0.854810 | ||||||||
\(556\) | 32.1269 | 1.36248 | ||||||||
\(557\) | 23.5539 | 0.998011 | 0.499005 | − | 0.866599i | \(-0.333699\pi\) | ||||
0.499005 | + | 0.866599i | \(0.333699\pi\) | |||||||
\(558\) | −11.3747 | −0.481529 | ||||||||
\(559\) | −33.2331 | −1.40561 | ||||||||
\(560\) | 6.25770 | 0.264436 | ||||||||
\(561\) | −1.49087 | −0.0629446 | ||||||||
\(562\) | −72.9974 | −3.07921 | ||||||||
\(563\) | 0.418547 | 0.0176397 | 0.00881983 | − | 0.999961i | \(-0.497193\pi\) | ||||
0.00881983 | + | 0.999961i | \(0.497193\pi\) | |||||||
\(564\) | 35.8898 | 1.51123 | ||||||||
\(565\) | −0.618676 | −0.0260279 | ||||||||
\(566\) | 70.1403 | 2.94822 | ||||||||
\(567\) | 6.58026 | 0.276345 | ||||||||
\(568\) | −57.5451 | −2.41454 | ||||||||
\(569\) | 18.3361 | 0.768688 | 0.384344 | − | 0.923190i | \(-0.374428\pi\) | ||||
0.384344 | + | 0.923190i | \(0.374428\pi\) | |||||||
\(570\) | 9.19409 | 0.385098 | ||||||||
\(571\) | −6.40194 | −0.267913 | −0.133956 | − | 0.990987i | \(-0.542768\pi\) | ||||
−0.133956 | + | 0.990987i | \(0.542768\pi\) | |||||||
\(572\) | −23.3958 | −0.978228 | ||||||||
\(573\) | −26.5695 | −1.10996 | ||||||||
\(574\) | −21.0407 | −0.878221 | ||||||||
\(575\) | −6.35308 | −0.264942 | ||||||||
\(576\) | 7.21011 | 0.300421 | ||||||||
\(577\) | −5.67089 | −0.236082 | −0.118041 | − | 0.993009i | \(-0.537661\pi\) | ||||
−0.118041 | + | 0.993009i | \(0.537661\pi\) | |||||||
\(578\) | 38.4826 | 1.60067 | ||||||||
\(579\) | −22.4862 | −0.934493 | ||||||||
\(580\) | −4.38145 | −0.181930 | ||||||||
\(581\) | 9.95199 | 0.412878 | ||||||||
\(582\) | 23.0641 | 0.956036 | ||||||||
\(583\) | 5.62092 | 0.232795 | ||||||||
\(584\) | 41.8761 | 1.73284 | ||||||||
\(585\) | −10.5025 | −0.434224 | ||||||||
\(586\) | −74.9982 | −3.09815 | ||||||||
\(587\) | −39.6616 | −1.63701 | −0.818504 | − | 0.574501i | \(-0.805196\pi\) | ||||
−0.818504 | + | 0.574501i | \(0.805196\pi\) | |||||||
\(588\) | −34.0152 | −1.40276 | ||||||||
\(589\) | −7.02934 | −0.289639 | ||||||||
\(590\) | 24.5449 | 1.01050 | ||||||||
\(591\) | 25.2769 | 1.03975 | ||||||||
\(592\) | 12.8966 | 0.530049 | ||||||||
\(593\) | 29.2391 | 1.20071 | 0.600353 | − | 0.799735i | \(-0.295027\pi\) | ||||
0.600353 | + | 0.799735i | \(0.295027\pi\) | |||||||
\(594\) | 13.6388 | 0.559606 | ||||||||
\(595\) | −2.44750 | −0.100338 | ||||||||
\(596\) | −11.6872 | −0.478725 | ||||||||
\(597\) | 38.0662 | 1.55795 | ||||||||
\(598\) | −69.6762 | −2.84927 | ||||||||
\(599\) | −0.362610 | −0.0148158 | −0.00740792 | − | 0.999973i | \(-0.502358\pi\) | ||||
−0.00740792 | + | 0.999973i | \(0.502358\pi\) | |||||||
\(600\) | −8.50643 | −0.347273 | ||||||||
\(601\) | 19.7417 | 0.805282 | 0.402641 | − | 0.915358i | \(-0.368092\pi\) | ||||
0.402641 | + | 0.915358i | \(0.368092\pi\) | |||||||
\(602\) | 13.0279 | 0.530976 | ||||||||
\(603\) | 3.10435 | 0.126419 | ||||||||
\(604\) | −45.3968 | −1.84717 | ||||||||
\(605\) | 25.1075 | 1.02076 | ||||||||
\(606\) | −54.9770 | −2.23329 | ||||||||
\(607\) | −10.6293 | −0.431432 | −0.215716 | − | 0.976456i | \(-0.569209\pi\) | ||||
−0.215716 | + | 0.976456i | \(0.569209\pi\) | |||||||
\(608\) | 2.40098 | 0.0973728 | ||||||||
\(609\) | −0.717693 | −0.0290824 | ||||||||
\(610\) | 3.02832 | 0.122613 | ||||||||
\(611\) | −38.9157 | −1.57436 | ||||||||
\(612\) | 2.42609 | 0.0980688 | ||||||||
\(613\) | −14.9268 | −0.602889 | −0.301444 | − | 0.953484i | \(-0.597469\pi\) | ||||
−0.301444 | + | 0.953484i | \(0.597469\pi\) | |||||||
\(614\) | 45.3306 | 1.82939 | ||||||||
\(615\) | 33.4207 | 1.34765 | ||||||||
\(616\) | 4.25540 | 0.171455 | ||||||||
\(617\) | −25.2249 | −1.01552 | −0.507759 | − | 0.861499i | \(-0.669526\pi\) | ||||
−0.507759 | + | 0.861499i | \(0.669526\pi\) | |||||||
\(618\) | 10.9669 | 0.441152 | ||||||||
\(619\) | −36.3429 | −1.46074 | −0.730372 | − | 0.683049i | \(-0.760653\pi\) | ||||
−0.730372 | + | 0.683049i | \(0.760653\pi\) | |||||||
\(620\) | 66.0732 | 2.65356 | ||||||||
\(621\) | 26.4439 | 1.06116 | ||||||||
\(622\) | 59.2470 | 2.37559 | ||||||||
\(623\) | −4.73996 | −0.189902 | ||||||||
\(624\) | −23.1259 | −0.925777 | ||||||||
\(625\) | −29.9190 | −1.19676 | ||||||||
\(626\) | −12.0366 | −0.481078 | ||||||||
\(627\) | 1.54983 | 0.0618944 | ||||||||
\(628\) | 57.3216 | 2.28738 | ||||||||
\(629\) | −5.04412 | −0.201122 | ||||||||
\(630\) | 4.11712 | 0.164030 | ||||||||
\(631\) | 8.68733 | 0.345837 | 0.172919 | − | 0.984936i | \(-0.444680\pi\) | ||||
0.172919 | + | 0.984936i | \(0.444680\pi\) | |||||||
\(632\) | 24.4794 | 0.973738 | ||||||||
\(633\) | −1.52449 | −0.0605930 | ||||||||
\(634\) | 26.7618 | 1.06285 | ||||||||
\(635\) | −9.43582 | −0.374449 | ||||||||
\(636\) | 31.4500 | 1.24707 | ||||||||
\(637\) | 36.8830 | 1.46136 | ||||||||
\(638\) | −1.13446 | −0.0449139 | ||||||||
\(639\) | −9.38510 | −0.371269 | ||||||||
\(640\) | −52.2344 | −2.06475 | ||||||||
\(641\) | −5.41728 | −0.213970 | −0.106985 | − | 0.994261i | \(-0.534120\pi\) | ||||
−0.106985 | + | 0.994261i | \(0.534120\pi\) | |||||||
\(642\) | −32.5017 | −1.28274 | ||||||||
\(643\) | −5.62772 | −0.221936 | −0.110968 | − | 0.993824i | \(-0.535395\pi\) | ||||
−0.110968 | + | 0.993824i | \(0.535395\pi\) | |||||||
\(644\) | 17.7824 | 0.700725 | ||||||||
\(645\) | −20.6932 | −0.814795 | ||||||||
\(646\) | 2.30292 | 0.0906070 | ||||||||
\(647\) | −46.6460 | −1.83384 | −0.916922 | − | 0.399066i | \(-0.869334\pi\) | ||||
−0.916922 | + | 0.399066i | \(0.869334\pi\) | |||||||
\(648\) | 27.0028 | 1.06077 | ||||||||
\(649\) | 4.13749 | 0.162411 | ||||||||
\(650\) | 19.8793 | 0.779731 | ||||||||
\(651\) | 10.8230 | 0.424185 | ||||||||
\(652\) | 30.5126 | 1.19497 | ||||||||
\(653\) | 42.2253 | 1.65240 | 0.826202 | − | 0.563374i | \(-0.190497\pi\) | ||||
0.826202 | + | 0.563374i | \(0.190497\pi\) | |||||||
\(654\) | −33.1334 | −1.29562 | ||||||||
\(655\) | −42.5351 | −1.66198 | ||||||||
\(656\) | −21.4030 | −0.835649 | ||||||||
\(657\) | 6.82961 | 0.266449 | ||||||||
\(658\) | 15.2555 | 0.594722 | ||||||||
\(659\) | 27.0148 | 1.05235 | 0.526173 | − | 0.850378i | \(-0.323626\pi\) | ||||
0.526173 | + | 0.850378i | \(0.323626\pi\) | |||||||
\(660\) | −14.5679 | −0.567053 | ||||||||
\(661\) | 41.5902 | 1.61767 | 0.808836 | − | 0.588034i | \(-0.200098\pi\) | ||||
0.808836 | + | 0.588034i | \(0.200098\pi\) | |||||||
\(662\) | 56.1529 | 2.18244 | ||||||||
\(663\) | 9.04497 | 0.351278 | ||||||||
\(664\) | 40.8390 | 1.58486 | ||||||||
\(665\) | 2.54430 | 0.0986637 | ||||||||
\(666\) | 8.48508 | 0.328790 | ||||||||
\(667\) | −2.19959 | −0.0851683 | ||||||||
\(668\) | 68.2671 | 2.64133 | ||||||||
\(669\) | −21.7343 | −0.840298 | ||||||||
\(670\) | −27.6983 | −1.07008 | ||||||||
\(671\) | 0.510480 | 0.0197068 | ||||||||
\(672\) | −3.69676 | −0.142606 | ||||||||
\(673\) | −42.6309 | −1.64330 | −0.821649 | − | 0.569993i | \(-0.806946\pi\) | ||||
−0.821649 | + | 0.569993i | \(0.806946\pi\) | |||||||
\(674\) | 61.2343 | 2.35866 | ||||||||
\(675\) | −7.54470 | −0.290396 | ||||||||
\(676\) | 93.4345 | 3.59363 | ||||||||
\(677\) | 3.45734 | 0.132876 | 0.0664382 | − | 0.997791i | \(-0.478836\pi\) | ||||
0.0664382 | + | 0.997791i | \(0.478836\pi\) | |||||||
\(678\) | −0.896292 | −0.0344219 | ||||||||
\(679\) | 6.38257 | 0.244940 | ||||||||
\(680\) | −10.0436 | −0.385154 | ||||||||
\(681\) | −18.9497 | −0.726155 | ||||||||
\(682\) | 17.1080 | 0.655098 | ||||||||
\(683\) | 47.2337 | 1.80735 | 0.903674 | − | 0.428222i | \(-0.140860\pi\) | ||||
0.903674 | + | 0.428222i | \(0.140860\pi\) | |||||||
\(684\) | −2.52204 | −0.0964326 | ||||||||
\(685\) | 53.4075 | 2.04059 | ||||||||
\(686\) | −31.3837 | −1.19823 | ||||||||
\(687\) | 33.6530 | 1.28394 | ||||||||
\(688\) | 13.2522 | 0.505236 | ||||||||
\(689\) | −34.1016 | −1.29917 | ||||||||
\(690\) | −43.3853 | −1.65165 | ||||||||
\(691\) | −4.24312 | −0.161416 | −0.0807080 | − | 0.996738i | \(-0.525718\pi\) | ||||
−0.0807080 | + | 0.996738i | \(0.525718\pi\) | |||||||
\(692\) | −54.5001 | −2.07178 | ||||||||
\(693\) | 0.694018 | 0.0263636 | ||||||||
\(694\) | 36.4582 | 1.38393 | ||||||||
\(695\) | −21.6910 | −0.822787 | ||||||||
\(696\) | −2.94513 | −0.111635 | ||||||||
\(697\) | 8.37114 | 0.317079 | ||||||||
\(698\) | −24.8671 | −0.941235 | ||||||||
\(699\) | 19.3351 | 0.731321 | ||||||||
\(700\) | −5.07349 | −0.191760 | ||||||||
\(701\) | 13.9967 | 0.528648 | 0.264324 | − | 0.964434i | \(-0.414851\pi\) | ||||
0.264324 | + | 0.964434i | \(0.414851\pi\) | |||||||
\(702\) | −82.7452 | −3.12302 | ||||||||
\(703\) | 5.24361 | 0.197767 | ||||||||
\(704\) | −10.8443 | −0.408709 | ||||||||
\(705\) | −24.2316 | −0.912616 | ||||||||
\(706\) | −54.2947 | −2.04341 | ||||||||
\(707\) | −15.2139 | −0.572178 | ||||||||
\(708\) | 23.1500 | 0.870029 | ||||||||
\(709\) | 29.4882 | 1.10745 | 0.553726 | − | 0.832699i | \(-0.313206\pi\) | ||||
0.553726 | + | 0.832699i | \(0.313206\pi\) | |||||||
\(710\) | 83.7376 | 3.14262 | ||||||||
\(711\) | 3.99237 | 0.149726 | ||||||||
\(712\) | −19.4509 | −0.728953 | ||||||||
\(713\) | 33.1702 | 1.24223 | ||||||||
\(714\) | −3.54576 | −0.132697 | ||||||||
\(715\) | 15.7961 | 0.590741 | ||||||||
\(716\) | −2.99497 | −0.111927 | ||||||||
\(717\) | −3.36331 | −0.125605 | ||||||||
\(718\) | −64.4451 | −2.40507 | ||||||||
\(719\) | 8.96886 | 0.334482 | 0.167241 | − | 0.985916i | \(-0.446514\pi\) | ||||
0.167241 | + | 0.985916i | \(0.446514\pi\) | |||||||
\(720\) | 4.18803 | 0.156079 | ||||||||
\(721\) | 3.03489 | 0.113025 | ||||||||
\(722\) | −2.39399 | −0.0890952 | ||||||||
\(723\) | 22.3591 | 0.831544 | ||||||||
\(724\) | 6.57085 | 0.244204 | ||||||||
\(725\) | 0.627563 | 0.0233071 | ||||||||
\(726\) | 36.3738 | 1.34996 | ||||||||
\(727\) | −21.0906 | −0.782207 | −0.391104 | − | 0.920347i | \(-0.627907\pi\) | ||||
−0.391104 | + | 0.920347i | \(0.627907\pi\) | |||||||
\(728\) | −25.8171 | −0.956845 | ||||||||
\(729\) | 30.0333 | 1.11234 | ||||||||
\(730\) | −60.9365 | −2.25536 | ||||||||
\(731\) | −5.18319 | −0.191707 | ||||||||
\(732\) | 2.85622 | 0.105569 | ||||||||
\(733\) | −26.2316 | −0.968887 | −0.484443 | − | 0.874823i | \(-0.660978\pi\) | ||||
−0.484443 | + | 0.874823i | \(0.660978\pi\) | |||||||
\(734\) | 55.3089 | 2.04149 | ||||||||
\(735\) | 22.9660 | 0.847112 | ||||||||
\(736\) | −11.3298 | −0.417623 | ||||||||
\(737\) | −4.66906 | −0.171987 | ||||||||
\(738\) | −14.0817 | −0.518354 | ||||||||
\(739\) | −26.4720 | −0.973789 | −0.486894 | − | 0.873461i | \(-0.661870\pi\) | ||||
−0.486894 | + | 0.873461i | \(0.661870\pi\) | |||||||
\(740\) | −49.2880 | −1.81186 | ||||||||
\(741\) | −9.40270 | −0.345417 | ||||||||
\(742\) | 13.3683 | 0.490767 | ||||||||
\(743\) | −17.0643 | −0.626030 | −0.313015 | − | 0.949748i | \(-0.601339\pi\) | ||||
−0.313015 | + | 0.949748i | \(0.601339\pi\) | |||||||
\(744\) | 44.4131 | 1.62826 | ||||||||
\(745\) | 7.89080 | 0.289096 | ||||||||
\(746\) | −42.2434 | −1.54664 | ||||||||
\(747\) | 6.66047 | 0.243694 | ||||||||
\(748\) | −3.64893 | −0.133418 | ||||||||
\(749\) | −8.99426 | −0.328643 | ||||||||
\(750\) | −33.5922 | −1.22661 | ||||||||
\(751\) | 39.5414 | 1.44289 | 0.721443 | − | 0.692474i | \(-0.243479\pi\) | ||||
0.721443 | + | 0.692474i | \(0.243479\pi\) | |||||||
\(752\) | 15.5183 | 0.565893 | ||||||||
\(753\) | 9.01049 | 0.328360 | ||||||||
\(754\) | 6.88269 | 0.250653 | ||||||||
\(755\) | 30.6505 | 1.11548 | ||||||||
\(756\) | 21.1178 | 0.768047 | ||||||||
\(757\) | −29.0014 | −1.05407 | −0.527037 | − | 0.849842i | \(-0.676697\pi\) | ||||
−0.527037 | + | 0.849842i | \(0.676697\pi\) | |||||||
\(758\) | −8.70287 | −0.316102 | ||||||||
\(759\) | −7.31340 | −0.265459 | ||||||||
\(760\) | 10.4408 | 0.378727 | ||||||||
\(761\) | −41.3892 | −1.50036 | −0.750180 | − | 0.661234i | \(-0.770033\pi\) | ||||
−0.750180 | + | 0.661234i | \(0.770033\pi\) | |||||||
\(762\) | −13.6699 | −0.495209 | ||||||||
\(763\) | −9.16908 | −0.331943 | ||||||||
\(764\) | −65.0291 | −2.35267 | ||||||||
\(765\) | −1.63802 | −0.0592226 | ||||||||
\(766\) | −40.8018 | −1.47423 | ||||||||
\(767\) | −25.1018 | −0.906372 | ||||||||
\(768\) | −43.1502 | −1.55705 | ||||||||
\(769\) | 15.0461 | 0.542578 | 0.271289 | − | 0.962498i | \(-0.412550\pi\) | ||||
0.271289 | + | 0.962498i | \(0.412550\pi\) | |||||||
\(770\) | −6.19231 | −0.223155 | ||||||||
\(771\) | −24.6434 | −0.887510 | ||||||||
\(772\) | −55.0352 | −1.98076 | ||||||||
\(773\) | 32.0186 | 1.15163 | 0.575814 | − | 0.817581i | \(-0.304685\pi\) | ||||
0.575814 | + | 0.817581i | \(0.304685\pi\) | |||||||
\(774\) | 8.71903 | 0.313399 | ||||||||
\(775\) | −9.46378 | −0.339949 | ||||||||
\(776\) | 26.1915 | 0.940220 | ||||||||
\(777\) | −8.07351 | −0.289635 | ||||||||
\(778\) | −21.3777 | −0.766429 | ||||||||
\(779\) | −8.70221 | −0.311789 | ||||||||
\(780\) | 88.3819 | 3.16458 | ||||||||
\(781\) | 14.1155 | 0.505093 | ||||||||
\(782\) | −10.8670 | −0.388605 | ||||||||
\(783\) | −2.61216 | −0.0933508 | ||||||||
\(784\) | −14.7077 | −0.525275 | ||||||||
\(785\) | −38.7017 | −1.38132 | ||||||||
\(786\) | −61.6217 | −2.19797 | ||||||||
\(787\) | 13.8389 | 0.493302 | 0.246651 | − | 0.969104i | \(-0.420670\pi\) | ||||
0.246651 | + | 0.969104i | \(0.420670\pi\) | |||||||
\(788\) | 61.8656 | 2.20387 | ||||||||
\(789\) | −39.7397 | −1.41477 | ||||||||
\(790\) | −35.6215 | −1.26736 | ||||||||
\(791\) | −0.248033 | −0.00881903 | ||||||||
\(792\) | 2.84797 | 0.101198 | ||||||||
\(793\) | −3.09703 | −0.109979 | ||||||||
\(794\) | −42.8876 | −1.52202 | ||||||||
\(795\) | −21.2340 | −0.753093 | ||||||||
\(796\) | 93.1676 | 3.30224 | ||||||||
\(797\) | −23.7849 | −0.842505 | −0.421252 | − | 0.906943i | \(-0.638409\pi\) | ||||
−0.421252 | + | 0.906943i | \(0.638409\pi\) | |||||||
\(798\) | 3.68600 | 0.130483 | ||||||||
\(799\) | −6.06948 | −0.214723 | ||||||||
\(800\) | 3.23251 | 0.114286 | ||||||||
\(801\) | −3.17227 | −0.112086 | ||||||||
\(802\) | −38.5182 | −1.36013 | ||||||||
\(803\) | −10.2720 | −0.362491 | ||||||||
\(804\) | −26.1242 | −0.921329 | ||||||||
\(805\) | −12.0061 | −0.423160 | ||||||||
\(806\) | −103.792 | −3.65593 | ||||||||
\(807\) | −23.5304 | −0.828310 | ||||||||
\(808\) | −62.4318 | −2.19634 | ||||||||
\(809\) | −53.1637 | −1.86914 | −0.934568 | − | 0.355784i | \(-0.884214\pi\) | ||||
−0.934568 | + | 0.355784i | \(0.884214\pi\) | |||||||
\(810\) | −39.2935 | −1.38063 | ||||||||
\(811\) | −24.3701 | −0.855750 | −0.427875 | − | 0.903838i | \(-0.640738\pi\) | ||||
−0.427875 | + | 0.903838i | \(0.640738\pi\) | |||||||
\(812\) | −1.75656 | −0.0616433 | ||||||||
\(813\) | 7.66593 | 0.268856 | ||||||||
\(814\) | −12.7619 | −0.447303 | ||||||||
\(815\) | −20.6011 | −0.721627 | ||||||||
\(816\) | −3.60683 | −0.126264 | ||||||||
\(817\) | 5.38819 | 0.188509 | ||||||||
\(818\) | −47.3708 | −1.65628 | ||||||||
\(819\) | −4.21054 | −0.147128 | ||||||||
\(820\) | 81.7975 | 2.85649 | ||||||||
\(821\) | −32.4003 | −1.13078 | −0.565389 | − | 0.824824i | \(-0.691274\pi\) | ||||
−0.565389 | + | 0.824824i | \(0.691274\pi\) | |||||||
\(822\) | 77.3728 | 2.69869 | ||||||||
\(823\) | 54.5118 | 1.90016 | 0.950082 | − | 0.312001i | \(-0.100999\pi\) | ||||
0.950082 | + | 0.312001i | \(0.100999\pi\) | |||||||
\(824\) | 12.4540 | 0.433854 | ||||||||
\(825\) | 2.08658 | 0.0726455 | ||||||||
\(826\) | 9.84026 | 0.342386 | ||||||||
\(827\) | 37.0810 | 1.28943 | 0.644716 | − | 0.764422i | \(-0.276975\pi\) | ||||
0.644716 | + | 0.764422i | \(0.276975\pi\) | |||||||
\(828\) | 11.9011 | 0.413590 | ||||||||
\(829\) | −18.0895 | −0.628274 | −0.314137 | − | 0.949378i | \(-0.601715\pi\) | ||||
−0.314137 | + | 0.949378i | \(0.601715\pi\) | |||||||
\(830\) | −59.4274 | −2.06276 | ||||||||
\(831\) | −8.38888 | −0.291007 | ||||||||
\(832\) | 65.7912 | 2.28090 | ||||||||
\(833\) | 5.75246 | 0.199311 | ||||||||
\(834\) | −31.4244 | −1.08814 | ||||||||
\(835\) | −46.0918 | −1.59507 | ||||||||
\(836\) | 3.79324 | 0.131192 | ||||||||
\(837\) | 39.3918 | 1.36158 | ||||||||
\(838\) | −32.1563 | −1.11082 | ||||||||
\(839\) | −30.5902 | −1.05609 | −0.528046 | − | 0.849216i | \(-0.677075\pi\) | ||||
−0.528046 | + | 0.849216i | \(0.677075\pi\) | |||||||
\(840\) | −16.0755 | −0.554658 | ||||||||
\(841\) | −28.7827 | −0.992508 | ||||||||
\(842\) | −31.1073 | −1.07203 | ||||||||
\(843\) | 46.4846 | 1.60101 | ||||||||
\(844\) | −3.73121 | −0.128433 | ||||||||
\(845\) | −63.0840 | −2.17015 | ||||||||
\(846\) | 10.2099 | 0.351024 | ||||||||
\(847\) | 10.0658 | 0.345865 | ||||||||
\(848\) | 13.5986 | 0.466976 | ||||||||
\(849\) | −44.6652 | −1.53290 | ||||||||
\(850\) | 3.10048 | 0.106345 | ||||||||
\(851\) | −24.7437 | −0.848202 | ||||||||
\(852\) | 78.9788 | 2.70577 | ||||||||
\(853\) | −12.5604 | −0.430061 | −0.215030 | − | 0.976607i | \(-0.568985\pi\) | ||||
−0.215030 | + | 0.976607i | \(0.568985\pi\) | |||||||
\(854\) | 1.21408 | 0.0415450 | ||||||||
\(855\) | 1.70280 | 0.0582345 | ||||||||
\(856\) | −36.9088 | −1.26152 | ||||||||
\(857\) | −13.5791 | −0.463852 | −0.231926 | − | 0.972733i | \(-0.574503\pi\) | ||||
−0.231926 | + | 0.972733i | \(0.574503\pi\) | |||||||
\(858\) | 22.8842 | 0.781255 | ||||||||
\(859\) | 1.04768 | 0.0357463 | 0.0178731 | − | 0.999840i | \(-0.494311\pi\) | ||||
0.0178731 | + | 0.999840i | \(0.494311\pi\) | |||||||
\(860\) | −50.6469 | −1.72705 | ||||||||
\(861\) | 13.3987 | 0.456625 | ||||||||
\(862\) | −75.9051 | −2.58534 | ||||||||
\(863\) | 32.8144 | 1.11701 | 0.558507 | − | 0.829500i | \(-0.311374\pi\) | ||||
0.558507 | + | 0.829500i | \(0.311374\pi\) | |||||||
\(864\) | −13.4549 | −0.457746 | ||||||||
\(865\) | 36.7967 | 1.25113 | ||||||||
\(866\) | −6.70366 | −0.227800 | ||||||||
\(867\) | −24.5056 | −0.832255 | ||||||||
\(868\) | 26.4893 | 0.899107 | ||||||||
\(869\) | −6.00467 | −0.203695 | ||||||||
\(870\) | 4.28564 | 0.145297 | ||||||||
\(871\) | 28.3267 | 0.959815 | ||||||||
\(872\) | −37.6262 | −1.27418 | ||||||||
\(873\) | 4.27160 | 0.144572 | ||||||||
\(874\) | 11.2968 | 0.382121 | ||||||||
\(875\) | −9.29604 | −0.314264 | ||||||||
\(876\) | −57.4735 | −1.94185 | ||||||||
\(877\) | −12.5291 | −0.423078 | −0.211539 | − | 0.977370i | \(-0.567848\pi\) | ||||
−0.211539 | + | 0.977370i | \(0.567848\pi\) | |||||||
\(878\) | 8.00888 | 0.270287 | ||||||||
\(879\) | 47.7587 | 1.61086 | ||||||||
\(880\) | −6.29895 | −0.212338 | ||||||||
\(881\) | −44.9832 | −1.51552 | −0.757761 | − | 0.652532i | \(-0.773707\pi\) | ||||
−0.757761 | + | 0.652532i | \(0.773707\pi\) | |||||||
\(882\) | −9.67663 | −0.325829 | ||||||||
\(883\) | 23.2820 | 0.783502 | 0.391751 | − | 0.920071i | \(-0.371869\pi\) | ||||
0.391751 | + | 0.920071i | \(0.371869\pi\) | |||||||
\(884\) | 22.1377 | 0.744571 | ||||||||
\(885\) | −15.6301 | −0.525400 | ||||||||
\(886\) | −28.5741 | −0.959965 | ||||||||
\(887\) | 11.0362 | 0.370559 | 0.185280 | − | 0.982686i | \(-0.440681\pi\) | ||||
0.185280 | + | 0.982686i | \(0.440681\pi\) | |||||||
\(888\) | −33.1304 | −1.11178 | ||||||||
\(889\) | −3.78291 | −0.126875 | ||||||||
\(890\) | 28.3042 | 0.948760 | ||||||||
\(891\) | −6.62364 | −0.221900 | ||||||||
\(892\) | −53.1951 | −1.78110 | ||||||||
\(893\) | 6.30953 | 0.211140 | ||||||||
\(894\) | 11.4316 | 0.382330 | ||||||||
\(895\) | 2.02210 | 0.0675915 | ||||||||
\(896\) | −20.9413 | −0.699599 | ||||||||
\(897\) | 44.3697 | 1.48146 | ||||||||
\(898\) | −29.4571 | −0.982997 | ||||||||
\(899\) | −3.27659 | −0.109280 | ||||||||
\(900\) | −3.39549 | −0.113183 | ||||||||
\(901\) | −5.31865 | −0.177190 | ||||||||
\(902\) | 21.1794 | 0.705197 | ||||||||
\(903\) | −8.29611 | −0.276077 | ||||||||
\(904\) | −1.01783 | −0.0338524 | ||||||||
\(905\) | −4.43642 | −0.147472 | ||||||||
\(906\) | 44.4041 | 1.47523 | ||||||||
\(907\) | −9.64206 | −0.320159 | −0.160080 | − | 0.987104i | \(-0.551175\pi\) | ||||
−0.160080 | + | 0.987104i | \(0.551175\pi\) | |||||||
\(908\) | −46.3797 | −1.53916 | ||||||||
\(909\) | −10.1821 | −0.337718 | ||||||||
\(910\) | 37.5681 | 1.24537 | ||||||||
\(911\) | 14.0619 | 0.465893 | 0.232946 | − | 0.972490i | \(-0.425163\pi\) | ||||
0.232946 | + | 0.972490i | \(0.425163\pi\) | |||||||
\(912\) | 3.74948 | 0.124158 | ||||||||
\(913\) | −10.0176 | −0.331534 | ||||||||
\(914\) | −37.7478 | −1.24859 | ||||||||
\(915\) | −1.92843 | −0.0637518 | ||||||||
\(916\) | 82.3662 | 2.72146 | ||||||||
\(917\) | −17.0527 | −0.563130 | ||||||||
\(918\) | −12.9054 | −0.425940 | ||||||||
\(919\) | −2.73360 | −0.0901730 | −0.0450865 | − | 0.998983i | \(-0.514356\pi\) | ||||
−0.0450865 | + | 0.998983i | \(0.514356\pi\) | |||||||
\(920\) | −49.2683 | −1.62433 | ||||||||
\(921\) | −28.8664 | −0.951181 | ||||||||
\(922\) | −31.1771 | −1.02676 | ||||||||
\(923\) | −85.6376 | −2.81880 | ||||||||
\(924\) | −5.84039 | −0.192135 | ||||||||
\(925\) | 7.05961 | 0.232119 | ||||||||
\(926\) | −19.8839 | −0.653426 | ||||||||
\(927\) | 2.03113 | 0.0667111 | ||||||||
\(928\) | 1.11917 | 0.0367386 | ||||||||
\(929\) | −48.4431 | −1.58937 | −0.794684 | − | 0.607024i | \(-0.792363\pi\) | ||||
−0.794684 | + | 0.607024i | \(0.792363\pi\) | |||||||
\(930\) | −64.6284 | −2.11925 | ||||||||
\(931\) | −5.97997 | −0.195985 | ||||||||
\(932\) | 47.3229 | 1.55011 | ||||||||
\(933\) | −37.7283 | −1.23517 | ||||||||
\(934\) | 56.3859 | 1.84500 | ||||||||
\(935\) | 2.46364 | 0.0805696 | ||||||||
\(936\) | −17.2784 | −0.564761 | ||||||||
\(937\) | 8.45475 | 0.276205 | 0.138102 | − | 0.990418i | \(-0.455900\pi\) | ||||
0.138102 | + | 0.990418i | \(0.455900\pi\) | |||||||
\(938\) | −11.1045 | −0.362575 | ||||||||
\(939\) | 7.66486 | 0.250133 | ||||||||
\(940\) | −59.3072 | −1.93439 | ||||||||
\(941\) | −23.8122 | −0.776257 | −0.388128 | − | 0.921605i | \(-0.626878\pi\) | ||||
−0.388128 | + | 0.921605i | \(0.626878\pi\) | |||||||
\(942\) | −56.0682 | −1.82680 | ||||||||
\(943\) | 41.0642 | 1.33723 | ||||||||
\(944\) | 10.0097 | 0.325789 | ||||||||
\(945\) | −14.2581 | −0.463815 | ||||||||
\(946\) | −13.1137 | −0.426364 | ||||||||
\(947\) | −54.0395 | −1.75605 | −0.878023 | − | 0.478618i | \(-0.841138\pi\) | ||||
−0.878023 | + | 0.478618i | \(0.841138\pi\) | |||||||
\(948\) | −33.5971 | −1.09118 | ||||||||
\(949\) | 62.3192 | 2.02297 | ||||||||
\(950\) | −3.22310 | −0.104571 | ||||||||
\(951\) | −17.0419 | −0.552620 | ||||||||
\(952\) | −4.02656 | −0.130502 | ||||||||
\(953\) | −41.5711 | −1.34662 | −0.673310 | − | 0.739361i | \(-0.735128\pi\) | ||||
−0.673310 | + | 0.739361i | \(0.735128\pi\) | |||||||
\(954\) | 8.94689 | 0.289666 | ||||||||
\(955\) | 43.9056 | 1.42075 | ||||||||
\(956\) | −8.23175 | −0.266234 | ||||||||
\(957\) | 0.722424 | 0.0233527 | ||||||||
\(958\) | 63.6416 | 2.05617 | ||||||||
\(959\) | 21.4115 | 0.691415 | ||||||||
\(960\) | 40.9662 | 1.32218 | ||||||||
\(961\) | 18.4116 | 0.593922 | ||||||||
\(962\) | 77.4251 | 2.49628 | ||||||||
\(963\) | −6.01950 | −0.193976 | ||||||||
\(964\) | 54.7242 | 1.76255 | ||||||||
\(965\) | 37.1580 | 1.19616 | ||||||||
\(966\) | −17.3936 | −0.559629 | ||||||||
\(967\) | −13.8825 | −0.446430 | −0.223215 | − | 0.974769i | \(-0.571655\pi\) | ||||
−0.223215 | + | 0.974769i | \(0.571655\pi\) | |||||||
\(968\) | 41.3061 | 1.32763 | ||||||||
\(969\) | −1.46649 | −0.0471105 | ||||||||
\(970\) | −38.1129 | −1.22373 | ||||||||
\(971\) | −40.8260 | −1.31017 | −0.655085 | − | 0.755556i | \(-0.727367\pi\) | ||||
−0.655085 | + | 0.755556i | \(0.727367\pi\) | |||||||
\(972\) | 25.6678 | 0.823294 | ||||||||
\(973\) | −8.69613 | −0.278785 | ||||||||
\(974\) | −36.4516 | −1.16798 | ||||||||
\(975\) | −12.6591 | −0.405416 | ||||||||
\(976\) | 1.23499 | 0.0395311 | ||||||||
\(977\) | 32.6035 | 1.04308 | 0.521540 | − | 0.853227i | \(-0.325358\pi\) | ||||
0.521540 | + | 0.853227i | \(0.325358\pi\) | |||||||
\(978\) | −29.8454 | −0.954351 | ||||||||
\(979\) | 4.77120 | 0.152488 | ||||||||
\(980\) | 56.2095 | 1.79555 | ||||||||
\(981\) | −6.13650 | −0.195923 | ||||||||
\(982\) | −51.6969 | −1.64972 | ||||||||
\(983\) | 49.1997 | 1.56923 | 0.784614 | − | 0.619984i | \(-0.212861\pi\) | ||||
0.784614 | + | 0.619984i | \(0.212861\pi\) | |||||||
\(984\) | 54.9827 | 1.75279 | ||||||||
\(985\) | −41.7697 | −1.33089 | ||||||||
\(986\) | 1.07346 | 0.0341859 | ||||||||
\(987\) | −9.71468 | −0.309222 | ||||||||
\(988\) | −23.0132 | −0.732148 | ||||||||
\(989\) | −25.4259 | −0.808496 | ||||||||
\(990\) | −4.14427 | −0.131713 | ||||||||
\(991\) | −45.9955 | −1.46110 | −0.730548 | − | 0.682862i | \(-0.760735\pi\) | ||||
−0.730548 | + | 0.682862i | \(0.760735\pi\) | |||||||
\(992\) | −16.8773 | −0.535856 | ||||||||
\(993\) | −35.7580 | −1.13475 | ||||||||
\(994\) | 33.5712 | 1.06481 | ||||||||
\(995\) | −62.9038 | −1.99418 | ||||||||
\(996\) | −56.0501 | −1.77602 | ||||||||
\(997\) | −42.4831 | −1.34545 | −0.672727 | − | 0.739891i | \(-0.734877\pi\) | ||||
−0.672727 | + | 0.739891i | \(0.734877\pi\) | |||||||
\(998\) | −39.6169 | −1.25405 | ||||||||
\(999\) | −29.3848 | −0.929693 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4009.2.a.e.1.6 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.e.1.6 | ✓ | 82 | 1.1 | even | 1 | trivial |